Singular Spectrum Analysis Library (SSALib)

Overview

The Singular Spectrum Analysis Library (SSALib) is a Python package for univariate (i.e., single) time series decomposition, designed for multidisciplinary applications like natural sciences, economics, epidemiology, and more. SSALib can be used to explore and extract trends, periodic patterns, and noise from time series.

Figure: Example of Decomposition and Pattern Extraction (standardized) using the Sea Surface Temperature Time Series

Key Features

• Univariate SSA implementation with both Broemhead & King and Vautard and Ghil approaches
• Multiple SVD solver options (NumPy, SciPy, scikit-learn)
• Monte Carlo SSA for significance testing
• Built-in visualization tools for analysis
• Include example datasets
• Comprehensive test coverage
• Type-annotated codebase

Quick Start

Requirements

• Python ≥ 3.9
• NumPy
• SciPy < 1.16.0
• Pandas
• Matplotlib
• Scikit-learn
• Statsmodels

Installation

Use

pip install git+https://github.com/ADSCIAN/ssalib.git

or

pip install ssalib

Basic Usage

from ssalib import SingularSpectrumAnalysis
from ssalib.datasets import load_sst

# Load example data: Mean Sea Surface Temperature
ts = load_sst()

# Create SSA instance and decompose
ssa = SingularSpectrumAnalysis(ts)
ssa.decompose()

# Visualize results, in this case, singular values
fig, ax = ssa.plot(kind='values')

# Reconstruct groups
ssa.reconstruct(groups={'trend': [0, 1], 'seasonality': [2, 3]})

# Export
df_ssa = ssa.to_frame()

Available Datasets

Dataset	Loading Function	Description	Time Range	Source	License
Mortality	load_mortality()	Daily counts of deaths in Belgium.	1992-01-01 to 2023-12-31	STATBEL	Open Data
SST	load_sst()	Monthly mean sea surface temperature globally between 60° North and South.	1982-01-01 to 2023-12-31	Climate Reanalyzer	CC-BY

Available SVD Methods

SSALib supports multiple SVD solvers:

Solver Name	Underlying Method	Status
numpy_standard	numpy.linalg.svd	Default
scipy_standard	scipy.linalg.svd	Available
scipy_sparse	scipy.sparse.linalg.svds	Available
sklearn_randomized	sklearn.utils.extmath.randomized_svd	Available

Select the solver with the svd_solver argument.

from ssalib import SingularSpectrumAnalysis
from ssalib.datasets import load_sst

# Load example data
ts = load_sst()

# Create SSA instance with solver 'sklearn_randomized'
ssa = SingularSpectrumAnalysis(ts, svd_solver='sklearn_randomized')

Available Visualizations

kind	Description	Decomposition Required	Reconstruction Required
matrix	Plot the matrix or its group reconstruction	Optional	Optional
paired	Plot pairs (x,y) of successive left-eigenvectors	Yes	No
periodogram	Plot periodogram associated with eigenvectors	Yes	No
timeseries	Plot original, preprocessed, or reconstructed time series	Optional	Optional
values	Plot the singular values ranked by value norm or dominant component frequency	Yes	No
vectors	Plot the left eigen vectors	Yes	No
wcorr	Plot the weighted correlation matrix	Yes	No

Pass the kind argument to the SingularSpectrumAnalysis.plot method.

Documentation

For more in-depth examples and tutorials, check the Jupyter notebooks in the notebooks folder:

• Tutorial 1: Introduction to SSA
• Tutorial 2: Plotting Guide
• Tutorial 3: SVD Matrix Construction and Window Sizes
• Tutorial 4: Comparison of SVD Solvers and Speed Performances
• Tutorial 5: Comparison of SSALib and Rssa

In more advanced tutorials, we cover:

• A1: Testing Significance with MonteCarloSSA

References

The main references used to develop SSALib were:

1. Golyandina, N., & Zhigljavsky, A. (2020). Singular Spectrum Analysis for Time Series. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-662-62436-4
2. Hassani, H. (2007). Singular Spectrum Analysis: Methodology and Comparison. Journal of Data Science, 5(2), 239–257. https://doi.org/10.6339/JDS.2007.05(2).396
3. Broomhead, D. S., & King, G. P. (1986). Extracting qualitative dynamics from experimental data. Physica D: Nonlinear Phenomena, 20(2), 217–236. https://doi.org/10.1016/0167-2789(86)90031-X
4. Vautard, R., & Ghil, M. (1989). Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D: Nonlinear Phenomena, 35(3). https://doi.org/10.1016/0167-2789(89)90077-8
5. Allen, M. R., & Smith, L. A. (1996). Monte Carlo SSA: Detecting irregular oscillations in the Presence of Colored Noise. Journal of Climate, 9(12), 3373–3404. https://doi.org/10.1175/1520-0442(1996)009<3373:MCSDIO>2.0.CO;2

How to Cite

Awaiting the release of the first non-beta version, you can refer to SSALib using:

@software{ssalib2025,
  author    = {Delforge, Damien AND Alonso, Alice AND de Viron, Olivier AND Vanclooster, Marnik AND Speybroeck, Niko},
  title     = {{SSALib}: A {Python} Library for {Singular Spectrum Analysis}},
  year      = {2025},
  version   = {0.1.2b1},
  url       = {https://github.com/ADSCIAN/ssalib}
}